Random Matrix Theory and Fund of Funds Portfolio Optimisation

The proprietary nature of Hedge Fund investing means that it is common practise for managers to release minimal information about their returns. The construction of a Fund of Hedge Funds portfolio requires a correlation matrix which often has to be estimated using a relatively small sample of monthly returns data which induces noise. In this paper random matrix theory (RMT) is applied to a cross-correlation matrix C, constructed using hedge fund returns data. The analysis reveals a number of eigenvalues that deviate from the spectrum suggested by RMT. The components of the deviating eigenvectors are found to correspond to distinct groups of strategies that are applied by hedge fund managers. The Inverse Participation ratio is used to quantify the number of components that participate in each eigenvector. Finally, the correlation matrix is cleaned by separating the noisy part from the non-noisy part of C. This technique is found to greatly reduce the difference between the predicted and realised risk of a portfolio, leading to an improved risk profile for a fund of hedge funds.Comment: 17 Page

Wavelet multiscale analysis for hedge funds: scaling and strategies

The wide acceptance of Hedge Funds by Institutional Investors and Pension Funds has led to an explosive growth in assets under management. These investors are drawn to Hedge Funds due to the seemingly low correlation with traditional investments and the attractive returns. The correlations and market risk (the Beta in the Capital Asset Pricing Model) of Hedge Funds are generally calculated using monthly returns data, which may produce misleading results as Hedge Funds often hold illiquid exchange-traded securities or difficult to price over-the- counter securities. In this paper, the Maximum Overlap Discrete Wavelet Transform (MODWT) is applied to measure the scaling properties of Hedge Fund correlation and market risk with respect to the S&P 500. It is found that the level of correlation and market risk varies greatly according to the strategy studied and the time scale examined. Finally, the effects of scaling properties on the risk profile of a portfolio made up of Hedge Funds is studied using correlation matrices calculated over different time horizons

Seizure characterisation using frequency-dependent multivariate dynamics

The characterisation of epileptic seizures assists in the design of targeted pharmaceutical seizure prevention techniques and pre-surgical evaluations. In this paper, we expand on recent use of multivariate techniques to study the crosscorrelation dynamics between electroencephalographic (EEG) channels. The Maximum Overlap Discrete Wavelet Transform (MODWT) is applied in order to separate the EEG channels into their underlying frequencies. The dynamics of the cross-correlation matrix between channels, at each frequency, are then analysed in terms of the eigenspectrum. By examination of the eigenspectrum, we show that it is possible to identify frequency dependent changes in the correlation structure between channels which may be indicative of seizure activity. The technique is applied to EEG epileptiform data and the results indicate that the correlation dynamics vary over time and frequency, with larger correlations between channels at high frequencies. Additionally, a redistribution of wavelet energy is found, with increased fractional energy demonstrating the relative importance of high frequencies during seizures. Dynamical changes also occur in both correlation and energy at lower frequencies during seizures, suggesting that monitoring frequency dependent correlation structure can characterise changes in EEG signals during these. Future work will involve the study of other large eigenvalues and inter-frequency correlations to determine additional seizure characteristics

Cross-correlation dynamics in financial time series

The dynamics of the equal-time cross-correlation matrix of multivariate financial time series is explored by examination of the eigenvalue spectrum over sliding time windows. Empirical results for the S&P 500 and the Dow Jones Euro Stoxx 50 indices reveal that the dynamics of the small eigenvalues of the cross-correlation matrix, over these time windows, oppose those of the largest eigenvalue. This behaviour is shown to be independent of the size of the time window and the number of stocks examined. A basic one-factor model is proposed, which captures the main dynamical features of the eigenvalue spectrum of the empirical data. Through the addition of perturbations to the one-factor model, (leading to a market plus sectors model), additional sectoral features are added, resulting in an Inverse Participation Ratio comparable to that found for empirical data

The branching of real lattice trees as dilute polymers

In this paper, the branching of real lattice trees is shown to be related to the occurrence of two different prefactor exponents. For all lattices where trivalent trees are embeddable, this exponent is estimated as being animal-like in nature. In addition, estimates for the growth parameter are given for a number of 2- and 3-dimensional lattices.On montre dans cet article que le branchement en arbres sur un réseau réel est lié à la présence des exposants de deux préfacteurs différents. Pour tous les réseaux où les arbres trivalents sont inscrits, cet exposant est estimé être de même nature que dans le cas des animaux. En outre, on donne des estimations du paramètre de croissance pour des réseaux à deux et trois dimensions

The perimeter in site directed percolation. Mean perimeter expansions

Exact expansions for susceptibility — like mean perimeter series for directed percolation and extended mean size series are analysed, on two and three dimensional lattices. The critical threshold pc estimates are refined for the triangular and simple cubic lattices. On the square next-nearest-neighbour site problem pc is estimated as pc = 0.4965 ± 0.002.Nous analysons des séries pour le périmètre moyen et la taille moyenne en percolation dirigée, séries dont nous avons obtenu des termes nouveaux. Nous obtenons des estimations plus précises pour le seuil de percolation critique pc dans le cas des réseaux triangulaires et cubiques. Dans le cas du problème de percolation de site avec seconds proches voisins sur le réseau carré, nous trouvons pc = 0,4965 ± 0,002

Effects of Viral Mutation on Cellular Dynamics in a Monte Carlo Simulation of HIV Immune Response Model in Three Dimensions

The cellular dynamics of HIV interaction with the immune system is explored in three-dimensions using a direct Monte Carlo simulation. Viral mutation with probability, Pmut, is considered with immobile and mobile cells. With immobile cells, the viral population becomes larger than that of the helper cells beyond a latency period Tcrit and above a mutation threshold Pcrit. That is at Pmut ≥ Pcrit, {Tcrit ∝ (Pmut − Pcrit)−γ}, with γ ≃ 0.73 in three dimensions and γ ⋍ 0.88 in 2-D. Very little difference in Pcrit is observed between two and three dimensions. With mobile cells, no power-law is observed for the period of latency, but the difference in Pcrit between two and three dimensions is increased. The time-dependency of the density difference between Viral and Helper cell populations (ρV − ρH) is explored and follows the basic pattern of an immune response to infection. This is markedly more defined than in the 2-D case, where no clear pattern emerges

Effect of Cellular Mobility on Immune Response

Mobility of cell types in our HIV immune response model is subject to an intrinsic mobility and an explicit directed mobility, which is governed by Pmob. We investigate how restricting the explicit mobility, while maintaining the innate mobility of a viral-infected cell, affects the model\u27s results. We find that increasing the explicit mobility of the immune system cells leads to viral dominance for certain levels of viral mutation. We conclude that increasing immune system cellular mobility indirectly increases the virus’ inherent mobility

Viral Load and Stochastic Mutation in a Monte Carlo Simulation of HIV

Viral load is examined, as a function of primary viral growth factor (P,) and mutation, through a computer simulation model for HIV immune response. Cell-mediated immune response is considered on a cubic lattice with four cell types: macrophage (M), helper (H), cytotoxic (C), and virus (V). Rule-based interactions are used with random sequential update of the binary cellular states. The relative viral load (the concentration of virus with respect to helper cells) is found to increase with the primary viral growth factor above a critical value (P,), leading to a phase transition from immuno-competent to immuno-deficient state. The critical growth factor (P,) seems to depend on mobility and mutation. The stochastic growth due to mutation is found to depend non-monotonically on the relative viral load, with a maximum at a characteristic load which is lower for stronger viral growth. (C) 2002 Elsevier Science B.V. All rights reserved

Visualization of complex biological systems: An immune response model using OpenGL

In this paper we present an update on our novel visualization technologies based on cellular immune interaction from both large-scale spatial and temporal perspectives. We do so with a primary motive: to present a visually and behaviourally realistic environment to the community of experimental biologists and physicians such that their knowledge and expertise may be more readily integrated into the model creation and calibration process. Visualization aids understanding as we rely on visual perception to make crucial decisions. For example, with our initial model, we can visualize the dynamics of an idealized lymphatic compartment, with antigen presenting cells (APC) and cytotoxic T lymphocyte (CTL) cells. The visualization technology presented here offers the researcher the ability to start, pause, zoom-in, zoom-out and navigate in 3-dimensions through an idealised lymphatic compartment